20 Great Mathematicians

8/2/2019 20 Great Mathematicians

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20

Great

Mathematicians

Submitted by:

Rejan Vincent U. Onting

Submitted to:

Mrs.Gwen Borje


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1.Isaac (Sir) Newton (1642-1727) England

Newton is so famous for his calculus, optics and laws of motion, it is easy to overlook

that he was also one of the greatest geometers. He solved the Delian cube-doublingproblem. Even before the invention of the calculus of variations, Newton was doingdifficult work in that field, e.g. his calculation of the "optimal bullet shape."

2. Archimedes of Syracuse (287-212 BC) Greek domain

Archimedes is universally acknowledged to be the greatest of ancient mathematicians.He studied at Euclid's school (probably after Euclid's death), but his work far surpassedthe works of Euclid. His achievements are particularly impressive given the lack of good

mathematical notation in his day. His proofs are noted not only for brilliance but forunequalled clarity, with a modern biographer (Heath) describing Archimedes' treatisesas "without exception monuments of mathematical exposition .

3. Johann Carl Friedrich Gauss (1777-1855) Germany

Carl Friedrich Gauss, the "Prince of Mathematics," exhibited his calculative powerswhen he corrected his father's arithmetic before the age of three. His revolutionarynature was demonstrated at age twelve, when he began questioning the axioms of

Euclid. His genius was confirmed at the age of nineteen when he proved that theregular n-gon was constructible, for odd n, if and only if n is the product of distinct primeFermat numbers.

4. Leonhard Euler (1707-1783) Switzerland

Euler may be the most influential mathematician who ever lived.His colleagues calledhim "Analysis Incarnate." Laplace, famous for denying credit to fellow mathematicians,once said "Read Euler: he is our master in everything." His notations and methods inmany areas are in use to this day. Euler was the most prolific mathematician in historyand is often judged to be the best algorist of all time.


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5. Georg Friedrich Bernhard Riemann (1826-1866) Germany

Riemann was a phenomenal genius whose work was exceptionally deep, creative and

rigorous; he made revolutionary contributions in many areas of pure mathematics, andalso inspired the development of physics. He had poor physical health and died at anearly age, yet is still considered to be among the most productive mathematicians ever.He was the master of complex analysis, which he connected to both topology andnumber theory, He applied topology to analysis, and analysis to number theory, makingrevolutionary contributions to all three fields.

6. Euclid of Megara & Alexandria (ca 322-275 BC) Greece/Egypt

Euclid may have been a student of Aristotle. He founded the school of mathematics atthe great university of Alexandria. He was the first to prove that there are infinitely manyprime numbers; he stated and proved the unique factorization theorem.

7. Jules Henri Poincar (1854-1912) France

Poincar was clumsy and frail and supposedly flunked an IQ test, but he was one of themost creative mathematicians ever, and surely the greatest mathematician of theConstructivist ("intuitionist") style. Poincar founded the theory of algebraic

(combinatorial) topology, and is sometimes called the Father of Topology (a title alsoused for Euler and Brouwer), but produced a large amount of brilliant work in manyother areas of mathematics.

8. Joseph-Louis (Comte de) Lagrange (1736-1813) Italy, France

Joseph-Louis Lagrange was a brilliant man who advanced to become a teen-ageProfessor shortly after first studying mathematics. He excelled in all fields of analysisand number theory; he made key contributions to the theories of determinants,continued fractions, and many other fields. He developed partial differential equationsfar beyond those of D. Bernoulli and d'Alembert, developed the calculus of variations farbeyond that of the Bernoullis, and developed terminology and notation (e.g. the useof f'(x) and f''(x) for a function's 1st and 2nd derivatives). He proved a fundamentalTheorem of Group Theory.


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9. David Hilbert (1862-1943) Prussia, Germany

Hilbert was preeminent in many fields of mathematics, including axiomatic theory,

invariant theory, algebraic number theory, class field theory and functional analysis. Hisexamination of calculus led him to the invention of "Hilbert space," considered one ofthe key concepts of functional analysis and modern mathematical physics. He was afounder of fields like metamathematics and modern logic

10. Gottfried Wilhelm von Leibniz (1646-1716) Germany

Leibniz pioneered the common discourse of mathematics, including its continuous,discrete, and symbolic aspects. (His ideas on symbolic logic weren't pursued and it wasleft to Boole to reinvent this almost two centuries later.) Mathematical innovations

attributed to Leibniz include the symbols ,df(x)/dx .

11. Alexandre Grothendieck (1928-) Germany, France

Grothendieck has done brilliant work in several areas of mathematics including numbertheory, geometry, topology, and functional analysis, but especially in the fields ofalgebraic geometry and category theory, both of which he revolutionized. He is mostfamous for his methods to unify different branches of mathematics, for example usingalgebraic geometry in number theory. Grothendieck is considered a master ofabstraction, rigor and presentation.

12. Pierre de Fermat (1601-1665) France

Fermat's most famous discoveries in number theory include the ubiquitously-used Fermat's Little Theorem; the n = 4case of his conjecturedFermat's LastTheorem(he may have proved the n = 3case as well); the fact that every naturalnumber is the sum of three triangle numbers; andFermat's Christmas Theorem(that any

prime (4n+1) can be represented as the sum of two squares in exactly one way,13. Niels Henrik Abel (1802-1829) Norway

At an early age, Niels Abel studied the works of the greatest mathematicians, foundflaws in their proofs, and resolved to reprove some of these theorems rigorously. Hewas the first to fully prove the general case of Newton's Binomial Theorem, one of themost widely applied theorems in mathematics. Perhaps his most famous achievement


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was the (deceptively simple) Abel's Theorem of Convergence (publishedposthumously), one of the most important theorems in analysis.

14. variste Galois (1811-1832) France

Galois, who died before the age of twenty-one, not only never became a professor, butwas barely allowed to study as an undergraduate. His output of papers, mostlypublished posthumously, is much smaller than most of the others on this list, yet it isconsidered among the most awesome works in mathematics. He applied group theoryto the theory of equations, revolutionizing both fields.

15. John von Neumann (1903-1957) Hungary, U.S.A.

Von Neumann pioneered the use of models in set theory, thus improving the axiomaticbasis of mathematics. He proved a generalized spectral theorem sometimes called themost important result in operator theory. He developed von Neumann Algebras. He was

first to state and prove the minimax theorem and thus invented game theory; this workalso advanced operations research. He invented cellular automata, famouslyconstructing a self-reproducing automaton. He invented elegant definitions for thecounting numbers (0 = {}, n+1 = n {n}). He also worked in analysis, matrix theory,measure theory, numerical analysis, ergodic theory, group representations, continuousgeometry, statistics and topology.

16. Karl Wilhelm Theodor Weierstrass (1815-1897) Germany

Weierstrass devised new definitions for the primitives of calculus and was then able toprove several fundamental but hitherto unproven theorems. He developed new insightsin several fields including the calculus of variations and trigonometry. He discovered theconcept of uniform convergence.

17. Ren Dscartes (1596-1650) France

Dscartes' early career was that of soldier-adventurer and he finished as tutor to royalty,but in between he achieved fame as the preeminent intellectual of his day. He isconsidered the inventor of analytic geometry and therefore the "Father of Modern

Mathematics." Because of his famous philosophical writings ("Cogito ergo sum") he isconsidered, along with Aristotle, to be one of the most influential thinkers in history.


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18. Brahmagupta `Bhillamalacarya' (589-668) Rajasthan (India)

Brahmagupta Bhillamalacarya (`The Teacher from Bhillamala') made great advances inarithmetic, algebra, numeric analysis, and geometry. Several theorems bear his name,including the formula for the area of a cyclic quadrilateral:

16 A2 = (a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d)Another famous Brahmagupta theorem dealing with such quadrilaterals can be phrased"In a circle, if the chords AB and CD are perpendicular and intersect at E, then the linefrom E which bisects AC will be perpendicular to BD." Proving Brahmagupta's theoremsare good challenges even today.

19. Carl G. J. Jacobi (1804-1851) Germany

Jacobi's most important early achievement was the theory of elliptic functions. He alsomade important advances in many other areas, including higher fields, number theory,algebraic geometry, differential equations, theta functions, q-series, determinants,Abelian functions, and dynamics. He devised the algorithms still used to calculateeigenvectors and for other important matrix manipulations.

20. Srinivasa Ramanujan Iyengar (1887-1920) India

Ramanujan's most famous work was with the partition enumeration function p(), Hardyguessing that some of these discoveries would have been delayed at least a centurywithout Ramanujan. Together, Hardy and Ramanujan developed an analyticapproximation to p(). (Rademacher and Selberg later discovered an exact expression toreplace the Hardy-Ramanujan formula; when Ramanujan's notebooks were studied itwas found he had anticipated their technique, but had deferred to his friend andmentor.)

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20 Great Mathematicians